Finding the Third Proportional to 256.78 and 397.69

Step by Step Solution

1. Step 1: Write the proportion equation
   256.78 : 397.69 = 397.69 : x
2. Step 2: Convert to fraction form
   256.78/397.69 = 397.69/x
3. Step 3: Cross multiply
   256.78x = 397.69 × 397.69
4. Step 4: Simplify right side
   256.78x = 158,155.35
5. Step 5: Solve for x
   x = 158,155.35/256.78
6. Step 6: Final answer
   x = 615.91